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The tangent complex to the Bloch-Suslin complex

Jean-Louis Cathelineau (2007)

Bulletin de la Société Mathématique de France

Motivated by a renewed interest for the “additive dilogarithm” appeared recently, the purpose of this paper is to complete calculations on the tangent complex to the Bloch-Suslin complex, initiated a long time ago and which were motivated at the time by scissors congruence of polyedra and homology of SL 2 . The tangent complex to the trilogarithmic complex of Goncharov is also considered.

Uniqueness of equivariant singular Bott-Chern classes

Shun Tang (2012)

Annales de l’institut Fourier

In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic classes, we will see that the construction of Bismut’s equivariant Bott-Chern singular currents provides a unique way to define a theory of equivariant singular Bott-Chern classes. This generalizes J. I. Burgos Gil and R. Liţcanu’s discussion...

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